Boundary regularity for \(p\)-harmonic functions and solutions of the obstacle problem on metric spaces

DOI10.2969/jmsj/1179759546zbMath1211.35109OpenAlexW1972054091MaRDI QIDQ861764

Jana Björn, Anders Björn

Publication date: 30 January 2007

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.jmsj/1179759546

zbMATH Keywords

metric spacenonlinearPoincaré inequalityobstacle problemregularbarriersuperharmonic\(p\)-harmonicdoubling

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Nonlinear elliptic equations (35J60) Regularity of solutions in optimal control (49N60) Boundary values of solutions to elliptic equations and elliptic systems (35J67) Other generalizations (nonlinear potential theory, etc.) (31C45)

Related Items (26)

Semiregular and strongly irregular boundary points for \(p\)-harmonic functions on unbounded sets in metric spaces ⋮ Necessity of a Wiener type condition for boundary regularity of quasiminimizers and nonlinear elliptic equations ⋮ Sphericalization and \(p\)-harmonic functions on unbounded domains in Ahlfors regular spaces ⋮ The obstacle and Dirichlet problems associated with p-harmonic functions in unbounded sets in R^n and metric spaces ⋮ Moser iteration for (quasi)minimizers on metric spaces ⋮ The Cartan, Choquet and Kellogg properties for the fine topology on metric spaces ⋮ BMO, integrability, Harnack and Caccioppoli inequalities for quasiminimizers ⋮ The Dirichlet problem for \(p\)-minimizers on finely open sets in metric spaces ⋮ Existence and almost uniqueness for \(p\)-harmonic Green functions on bounded domains in metric spaces ⋮ Cluster sets for Sobolev functions and quasiminimizers ⋮ Regularity of \(p(\cdot)\)-superharmonic functions, the Kellogg property and semiregular boundary points ⋮ Reverse Khas'minskii condition ⋮ Weak barriers in nonlinear potential theory ⋮ Harnack's principle for quasiminimizers ⋮ The obstacle problem for the \(p\)-Laplacian via optimal stopping of tug-of-war games ⋮ The Kellogg property and boundary regularity forp-harmonic functions with respect to the Mazurkiewicz boundary and other compactifications ⋮ A regularity classification of boundary points for \(p\)-harmonic functions and quasiminimizers ⋮ Fine continuity on metric spaces ⋮ Lebesgue points and the fundamental convergence theorem for superharmonic functions on metric spaces ⋮ Convergence results for obstacle problems on metric spaces ⋮ Continuous dependence on obstacles for the double obstacle problem on metric spaces ⋮ Global integrability of \(p\)-superharmonic functions on metric spaces ⋮ Boundary regularity for p-harmonic functions and solutions of obstacle problems on unbounded sets in metric spaces ⋮ Nonlinear balayage on metric spaces ⋮ On the equivalence of stochastic completeness and Liouville and Khas’minskii conditions in linear and nonlinear settings ⋮ Obstacle and Dirichlet problems on arbitrary nonopen sets in metric spaces, and fine topology

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